A new fundamental equation for the band spectra of dielectric layer films

Frank Szmulowicz

doi:10.1117/12.809262

16 February 2009 A new fundamental equation for the band spectra of dielectric layer films

Frank Szmulowicz

Proceedings Volume 7223, Photonic and Phononic Crystal Materials and Devices IX; 72230S (2009) https://doi.org/10.1117/12.809262
Event: SPIE OPTO: Integrated Optoelectronic Devices, 2009, San Jose, California, United States

Abstract

This paper derives a new fundamental equation for the frequency spectra ω(q) of one-dimensional photonic crystals as a function of Brillouin wave vector q in the form of a novel factored expression, tan² qd / 2 = tan(k_Na_N -α_N) × tan(k_Na_N - β_N), where N the number of layers per period is, d is the unit cell width, and k_i = n_iω/c is the local wave vector in the ith layer of width 2a_i and refractive index n_i. Angles(α_N,β_N) depend on the parameters of all N layers but are independent of a_N . For two layers, (α₂, β₂) correspond to the even/odd parity solutions at the center and the edge of the Brillouin zone. The derived spectral expression provide separate eigenvalue conditions for consecutive band edges at the center and the edge of the Brillouin zone for any N and is useful in finding the Bloch phase that is necessary in finite crystal calculations. The formalism is convenient for tailoring band gaps and for calculating impurity modes in dielectric stacks.

Citation Download Citation

Frank Szmulowicz "A new fundamental equation for the band spectra of dielectric layer films", Proc. SPIE 7223, Photonic and Phononic Crystal Materials and Devices IX, 72230S (16 February 2009); https://doi.org/10.1117/12.809262

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available